Theorem 4: If one pair of opposite sides in a four sided figure are both opposite and parallel, then the figure is a parallelogram.

Given: AB || DC

AB = DC

To prove: ABCD is a parallelogram.

First we draw in the diagonal

There are two ways to prove this result. If we can prove that the other pair of sides are parallel, then the result will follow from the definition of a parallelogram.

Another method would be to prove that the other pair of sides is congruent. The result would then follow from Theorem 2.